1976•International Journal for Numerical Methods in EngineeringRequires access

Calculation of eigenvalues of the Helmholtz equation by an integral equation

Gilbert De Mey

Abstract

Abstract A method is presented to calculate the eigenvalues of the Helmholtz equation Δ2ø + k2ø = 0 in a two‐dimensional area when ø vanishes on the boundary. The method is based on an integral equation, which can be easily solved numerically. Results obtained for circular and rectangular geometries are also given and compared to the exact values.

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Available abstract

Key concepts: Helmholtz equation, Eigenvalues and eigenvectors, Mathematics, Electric-field integral equation, Mathematical analysis, Integral equation, Helmholtz free energy, Summation equation